The prior art to the current invention is embodied in particular by one recent published paper by Tinker, “Occult Parasitic Energy Loss in Heat Engines”, Frank A. Tinker, International Journal of Energy Research, 2007:31, 1441-1453 [1], U.S. Pat. No. 7,441,530 to Tinker [2], and US patent publication 2007/0227347, also to Tinker [3]. This paper by Tinker and his two patent publications are incorporated in their entirety by reference. The prior art on thermal engines is immense, but a subset most pertinent to the current disclosures is presented in the listing of prior art patents.
After decades of large research and engineering investments, thermal engines, to include Diesel engines, are indeed improved from their earlier designs. But the improvements in efficiency have been disappointing and are disproportionate to the large amounts of time, money and intellectual energy invested. It is this applicant's contention that achievement of significant further improvements in thermal engine efficiency will require abandonment of the conventional engine designs, most of which are today well over 100 years old. In their place we will develop new, creative and innovative solutions derived from new insights into the physics of thermal engines. Recent rises in oil prices make this the right time to examine radical departures from “old engine” technology.
Thermal engines are almost as old as the science of Thermodynamics itself. Yet, after well over at least 100 years of concerted effort, there are few (arguably none) thermal engines that even come close to approaching the theoretically possible thermal to mechanical conversion efficiency. With few (if any) exceptions, they almost all suffer from thermal efficiency that is markedly below that which should be theoretically obtainable from their specific power (heat) source.
In Tinker [1], a new thermodynamic theory of thermal engines is developed and proved with experimental data. The key element of Tinker's new discovery is that remarkably, the efficiency of the Carnot Cycle has been incorrectly derived by thousands of physicists for over a hundred years. It would seem that all before Tinker have ignored the rather obvious fact that the input work for each Carnot Cycle compression phase must come from “somewhere”, and that “somewhere” must be from a portion of the engine's own output work in a prior expansion phase. Therefore the real available net output work is in reality less by an amount equal to the compression work. As can be easily appreciated, this then reduces the efficiency of the thermal engine from what might have been expected otherwise. Tinker's modified new theory correctly predicts a lower engine efficiency than other prior theories. Tinker's new theory also aligns almost perfectly with carefully conducted experiments whose data have long been in the literature. Practitioners have apparently ignored these data, or at least attributed their deviations from prediction to other possible effects, no doubt in part because such other theories did not predict these data until presented in Tinker [1] and further disclosed in Tinker [2] and to a lesser extent Tinker [3] which also presented the corrected new theory.
In Tinker [2], a means is proposed to improve the efficiency of thermal engines using his new theory. Although Tinker [2] also presents elements of the new theory for the efficiency of heat engines, its focus is on a mechanical addition that is claimed to improve the efficiency of the engine by recovering energy between cycles in the engine. The mechanical addition is claimed to neutralize the compressive force through the use of a conservative force, thereby driving the compressive work to zero and hence improving the efficiency of the engine significantly. But it is not at all clear (at least to this applicant) within the context of Tinker's new theory, how the patent of Tinker [2] is supposed to work. The claimed conservative force, while indeed reducing the compression work, must also of necessity (since it is conservative) reduce the output work by the same amount saved during compression in order to “recharge” the conservative force. In effect this is the same mechanism as the venerable flywheel, and only serves to keep the engine operating more smoothly and at lower rotation speeds. To the extent that the “conservative force” might implement a custom contoured compression pressure profile resulting in improved efficiency is also not at all clear (at least to this applicant) from Tinker [2].
In Tinker [3], again the concept of neutralizing the compressive work through a conservative force is promulgated. But this time the use of orthogonal pistons and cylinders held in a specifically defined geometry is proposed to produce the claimed conservative force that exactly balances the compressive force. Again, it is not at all clear how this scheme is supposed to work, for any force applied to counter the compression force must derive from an expansion force from an earlier or later cycle.
Given the points above, one is drawn to conclude that Tinker has made a very significant discovery, but despite Tinker [2], until more evidence to the contrary, this applicant fails to see how the scheme in Tinker [2] or Tinker [3] capitalizes on this new discovery visa vie a viable physically realizable thermal engine with significantly higher efficiency. It is therefore a first objective of the current invention to disclose pragmatic, realizable and significant improvements in thermal engines either enabled by and/or inspired by Tinker [1]. These improvements may be instantiated singly for modest improvements in efficiency, but preferably employed collectively or at least in subsets of cooperative improvements which introduce synergisms to improve the efficiency than beyond that of individual improvements alone or in few.
It is a second objective of the current invention to disclose a method for deriving the design of an optimally efficient engine based on the first principles efficiency equation given in Tinker [1], combined with the systems requirements and constraints of the engine under design. This is illustrated using the well-known Calculus and Spectral Signal Processing techniques such as the Fourier Transform. It is shown how the practitioner can use this method to derive a candidate instantiation mechanism for an engine that would meet a set of top level design requirements and constraints by transforming the thermodynamic design into a set of mechanical cycle bases, not unlike the way orthogonal functions such as Sines and Cosines can be combined in Fourier Series to produce desired functional forms. In a like manner, the volume for the mechanical operation of a thermodynamic cycle can be synthesized by the intelligent combination of basis cyclic mechanisms. The result is a basic design of the mechanism that will instantiate the volume profile for an optimally efficiency engine. That is, given a set of descriptive equations for a maximally efficient engine, the current invention quantitatively determines a mechanical mechanism that will instantiate these equations into a maximally efficient thermal engine embodiment. Through this method, the practitioner of engine design may enjoy a significantly streamlined design process that both encompasses all the multiple optimization criteria needed in modern engines (emissions constraints, temperature constraints, friction constraints, etc.) as well as the most straight forward mechanical embodiments for engines which meet these multiple criteria with maximal thermal efficiency and simplicity of mechanical design.
It is a third objective of the current invention is to use the enabling theory and insights of Tinker [1], the new improvements disclosed from the first objective, as well as the combination of these and other known improvements, and through the method of design illustrated after the second objective, to then develop and disclose some specific designs of improved thermal engines that are at least significantly more efficient than other engines currently in the art, and which arguably can begin to approach the maximally efficient Carnot Cycle efficiency. Although some of these engines may bear some resemblance to current engine designs or proposals, they are significantly different in the important ways needed to optimize efficiency to the end of achieving high double digit efficiency values, nominally greater than 50%, that are otherwise not achievable without the teachings presented herein.
Back To Basics: The Carnot Cycle
We begin with a basic refresher on thermal engine thermodynamic efficiency. There is nothing new or novel in this review and the details are available in books on thermodynamics, as should be apparent to one skilled in the art. All thermal engines operate on a cycle that accepts heat in from a hot temperature source and discharges waste heat to a cold temperature sink. The intervening thermal engine converts some of the heat from the hot source to mechanical work. For maximum efficiency we seek to maximize the work extracted from the engine and minimize the waste heat. An immediate outcome of the Second Law of Thermodynamics applied to thermal engines teaches that we can never reduce the waste heat to zero, and consequently we can never realize a thermal engine with perfect (100%) conversion efficiency of input heat energy to output work. However, we can potentially achieve a theoretically limited efficiency only somewhat less than 100%. This theoretical maximum efficiency is given by the well-known Carnot Cycle as shown in FIGS. 1a and 1b. 
It is a fundamental result of Thermodynamics that a Carnot Cycle gives the maximum theoretically possible efficiency for a thermal engine: there is no cycle that can be more efficient than a Carnot Cycle. FIG. 1a shows the Pressure-Volume, and Temperature-Entropy is shown in FIG. 1b. This particular cycle was computed in MATLAB using a normalized set of units to aid in seeing the relative magnitudes of the variables. Note that in what follows, all processes are assumed to be perfect and reversible in accordance with the assumptions used to analyze the Carnot Cycle.
The cycle begins at point “1” which has a Pressure, P1, equal to 1; a Volume, V1, equal to 10; a Temperature, T1, equal to 10; and an Entropy, S1, of 1.4 (related to the Specific Heat Ratio, representatively assumed to be 1.4). From point “1” the Carnot Cycle executes an Isothermal Compression that goes to point “2”. During this phase of the Carnot Cycle work is done on the system and heat is extracted from the system. Compression progresses at just the right rate to compensate for the heat lost to the cold sink in such a manner to maintain the working gas of the engine at a constant temperature. Conversely, the rate of heat extracted might be adjusted to the mechanical compression performed, again to the purpose of maintaining the temperature constant.
Next, the working gas undergoes an Adiabatic Compression from point “2” to point “3”. During this phase mechanical work is applied to the working gas to compress it without input or extraction of heat. Because no heat can escape, the temperature therefore rises, and as the volume decreases the pressure rises. This phase of the Carnot Cycle ends with the system in a state of maximum compression where the Volume, V3, is 1; the Temperature, T3, is 100; the Pressure, P3, is 14, and the Entropy, S3 is 0 (all in our normalized units). This point represents the most mechanically stressing part of the cycle due to the confluence of highest pressure and highest temperature in the cycle.
The third phase of the cycle takes it from point “3” to point “4” under an Isothermal Expansion. It is during this phase that the heat is added to the engine, some of which will be converted to the desired output work in accordance with the engine's efficiency. The working gas temperature during this phase of the cycle, T3→T4, is maintained at a temperature of 100 by adding just enough heat to compensate for the mechanical expansion, or conversely by expanding at just the right rate to compensate for the rate of heat being input.
Finally, an Adiabatic Expansion takes the cycle from point “4” back the beginning at point “1”. More work is extracted during this phase but there is no additional heat allowed to enter, or exit, the engine during this expansion. At the end of this last phase the engine is back in the state it was in the beginning, ready for another work producing cycle.
The Carnot Cycle produces the highest theoretically possible efficiency between a given heat source and a given heat sink: no other engine cycle can exceed it. This efficiency is given by:
  η  =      1    -                  T        c                    T        h            Where η is the efficiency, Th is the temperature of the hot thermal source (T3 in FIG. 1) and Tc is the temperature of the cold sink (T1 in FIG. 1).Realization of Carnot Cycle
At this point we summarize the well-established physics described in the prior section looking for insight to higher efficiency thermal engines:                All thermal engines must execute a “cycle” to convert heat energy into work energy.        This conversion can never be done with perfection: there will always be some waste heat.        A perfect efficiency thermal engine is therefore impossible without violating physical laws.        The highest efficiency that any thermal engine might ever attain is described fully by a Carnot Cycle: no other thermal engine can ever exceed this theoretical efficiency.The Carnot Cycle is proven to produce the highest theoretical efficiency possible for any thermal engine. So all that is needed is to use a Carnot Cycle engine, and we then know a priori that we are obtaining the highest efficiency possible. Appropriate modifications can then be made to consciously trade some of that efficiency for other desirable attributes such as power, fuel, etc.However, there is no “Carnot Cycle Engine”. And therein lies the issue. There are Otto Cycle engines, Diesel Cycle Engines, Rankine Cycle engines, Brayton Cycle Engines, Humphreys Cycle Engines, Atkinson Cycle Engines, Miller Cycle Engines and a host of lesser well-known cycles. But to our knowledge there are no overt “Carnot Cycle Engines”. And therefore, we can be certain that higher efficiency thermal engines can be built than any of the engines mentioned above.        
But why are there no overt Carnot Cycle thermal engines? To be sure, no machine is perfect, and therefore due to friction and other practicalities we cannot really make a perfect Carnot Cycle engine. But within the limits imposed by these practical considerations we should be able to make a Pseudo-Carnot Cycle engine with close to optimum theoretical efficiency. So the question remains, why is there not a Carnot Cycle engine?
The answer to this question appears to be foggy at best. It may simply be a perception that design and development of a Carnot Cycle engine is somehow far more difficult that other cycle engines. This perception dates back some time (at least to 1946) as evidenced by reference [4], page 180, containing the following passage regarding implementation of the Carnot cycle:                “Although it may appear from the analysis that the Carnot Cycle is highly impractical, since an engine working under the specified conditions could not be built . . . ”.But there are no physical laws prohibiting the construction of a near ideal Carnot Cycle engine, and the success of the Otto Cycle engine is ample proof that even an imperfect Carnot Cycle engine that does not perfectly meet its theoretically limited efficiency could be quite successful.        
The reason for the apparent perception of Carnot Cycle engine impracticality was perhaps because of the limited manufacturing capabilities of the day when thermo-engine research was young and at its peak development. But it is important to note that what “could not be built” back in 1946 (or earlier) can today be programmed into a CNC machine and reproduced economically a thousand-fold without error. Therefore, the constraints limiting the realization of a pragmatic and economically manufacturable Carnot Cycle or Carnot-like thermal engine that may have existed in the past, no longer necessarily constrain its development today or in the future.
Furthermore, if one seeks other attributes like power, weight, etc., one may have to trade away some of the ideal Carnot Cycle efficiency to obtain those attributes. But in doing so one will have designed in those attributes as trade-offs to the engine efficiency instead of just accepting them post facto. In such a case one can then design the highest efficiency thermal engine that also achieves the desired additional attributes, using the desired attributes as constraints to the efficiency of the now most efficient pseudo-Carnot Cycle. The difference between this engine and others before it is that it will be fully optimized.
At this point it is believed instructive to briefly review some of the more common thermal cycles so they can be compared to the Carnot Cycle and evaluated against it. Arguably the most common (and successful) thermal cycle is the Otto Cycle shown in FIG. 2, and in other detail with its intake and exhaust cycles shown, in FIGS. 4a and 4b. 
Comparing FIG. 2 with FIG. 1, one thing is immediately apparent (yet seldom really fully acknowledged): The Otto Cycle is NOT a Carnot Cycle. It does not even do a particularly good job of mimicking a Carnot Cycle.                Heat is not withdrawn gradually and isothermally in the early part of the compression stroke        Heat is added all at once from the heat source in an Isochoric (Isovolume) process        Heat is not added gradually and isothermally in the early part of the expansion stroke        Heat is released to the cold sink all at once in an Isochoric process at the end of the cycleThe Otto Cycle is therefore a rather poor emulation of a Carnot Cycle and so distorts the Carnot Cycle that we should be surprised that it provides any worthwhile efficiency at all! Yet, car manufacturers have spent untold millions of dollars trying to glean minute efficiency improvements from a cycle that is fundamentally and irrevocably flawed as far as optimizing efficiency is concerned. It is of course acknowledged that there are many good reasons for the Otto Cycle's success, not the least of which is ease of manufacturability as previously noted. But what we see in the above discussion is that when it comes to efficiency, we have reached a point of diminishing returns trying to improve the Otto Cycle if for no other reason that the Otto Cycle is not a Carnot Cycle nor even a good approximation of a Carnot Cycle.The efficiency of the Otto Cycle is given by:        
  η  =            1      -                        T          1                          T          2                      =          1      -              1                  r                      γ            -            1                              where T1 is the sink temperature, T2 is the pre-combustion compression temperature, r is the compression ratio and gamma is the specific heat ratio. Because of this latter relation, it is often claimed that the efficiency of the Otto Cycle is related to the compression ratio: higher compression ratio begets higher efficiency (ergo the Diesel engine is generally (but not necessarily always) more efficient than the Gasoline Otto engine).
It should be pointed out though that this is a deduced result, not the fundamental result. It is important to now note that the Carnot Cycle's efficiency is 1−T1/T3 (in the nomenclature of FIGS. 1a, 1b and 2), not 1−T1/T2 as for the Otto Cycle. In other words, the Carnot Cycle's efficiency is dependent only on the temperatures of the heat sink and the heat source. But the Otto Cycle's efficiency is related only to the temperature of its heat sink and its pre-combustion compression temperature. This pre-combustion compression temperature is much lower than the peak temperature (T3) in FIGS. 1a, 1b and 2 (assumed to be equal in both figures), and consequently, the Otto Cycle is guaranteed to be less efficient than the Carnot Cycle by a non-trivial amount.
Comparing the Carnot Cycle with the Other Cycles
The general conclusions discussed above are not limited to the Otto Cycle. Rather, all the currently popular thermal cycles suffer similar deleterious efficiency degradations inherent in the basic design of their cycles. This is because, by definition, they are not Carnot Cycles. The Diesel Cycle is actually quite similar to the Otto Cycle. The key difference is that it replaces the trans-ignition Isochoric compression with an isobaric (constant pressure) “cap” to the P-V diagram as illustrated in FIGS. 3a and 3b. The efficiency of the Diesel Cycle is given by:
  η  =      1    -                  1        γ            ⁢                                    (                          1              r                        )                                γ            -            1                          ⁡                  [                                                    r                co                γ                            -              1                                                      r                co                            -              1                                ]                    where η is again the efficiency, Gamma is the ratio of specific heats, r is the compression ratio, and rco is the (Diesel injector) cut-off volume ratio (V3/V2). This equation is a bit more difficult to assess qualitatively, but considering limits helps. In the limit where the cut off ratio, rco, goes to 1, the Diesel efficiency achieves its maximum. This should not be surprising because then the top left corner of the P-V diagram of FIG. 3a starts looking like a Carnot Cycle. However, if V3=V2, this means the injector never injects any fuel into the cylinder! That of course results in very low power output and a rather useless engine (even if it does have higher efficiency).
Beyond this unrealistic limit, the Diesel Cycle does generally end up being more efficient than the Otto Cycle on a comparative basis. But note why this is true. There is still no isothermal path in the beginning of the compression stroke, nor is there an isothermal expansion at the beginning of the expansion stroke, and the heat is still being pulled out at the wrong place in the cycle through an isochoric process at the end of the cycle. But at least the heat is now being added in the beginning of the expansion phase. Its still not an adiabatic expansion as called for in the Carnot Cycle, but at least the heat is being added in the correct phase of the cycle. Because of this, the Diesel Cycle more closely resembles the Carnot Cycle than the Otto Cycle, and with its higher compressing ratios is more efficient as a result.
FIGS. 5a and 5b show the Miller Cycle is a modification of the Otto and Diesel Cycles wherein some of the compressive work is lessened by letting the intake valve stay open for a short period past the bottom dead center of the intake stroke. This lets some of the air fuel mixture escape back out into the intake manifold where (assuming a good supercharger) it can return the energy on the next intake stroke. compared to the Otto Cycle. Note that other than a small corner near the start of the cycle (i.e. what we have been calling position “1”), there is no difference between the Miller Cycle and the Otto Cycle. To be sure, the Miller Cycle is indeed more efficient than a standard comparable Otto Cycle. But this is not because the cycle is fundamentally more efficient. Rather, it is simply because the Miller Cycle, if implemented correctly (which apparently is not a trivial thing to do) reduces the intake and exhaust pumping losses.
Note that we have not shown the pumping cycles in any figures to this point, because they are not part of the fundamental cycle physics that limits the efficiency. Therefore, the Miller Cycle certainly does improve the efficiency of either Otto or Diesel engines, but not because of any change real to the fundamental thermodynamic cycle. The underlying cycle is still not a Carnot Cycle and it is therefore still suboptimal. All the Miller Cycle really does is to reduce some instantiation losses to get a little closer to the theoretical efficiency of the Otto and Diesel Cycles respectively.
The Atkinson cycle (FIG. 6) produces two different compressed volumes at the two Top Dead Center (TDC) positions that occur in its 4 stroke cycle process. This manifests a slightly longer power stroke, a near zero volume at top dead center of the exhaust stroke for more complete exhaustion of the burnt gases, and a slightly lower pumping loss upon compression of the air-fuel mixture provided by a slightly shorter compression stroke that leave more volume at top dead center of the compression stroke than at top dead center of the exhaust stroke. It is this later feature that is often confused with the Miller Cycle and visa-versa. The Miller Cycle achieves lower pumping losses by cheating (leaving the intake valve open longer than typical in an Otto Cycle engine). In the Atkinson Cycle, lower pumping loss is achieved because the intake phase volume is actually smaller than the expansion phase (power stroke) volume. There is a differential embodiment of the Atkinson Engine with two pistons exhibiting in dual volumes behavior described above.
The Brayton and Humphrey Cycles are shown comparatively in FIGS. 7a and 7b. The Brayton Cycle is characterized by two constant pressure phases in the cycle. The high temperature phase mimics that of a Diesel, so we should expect some higher efficiency from that aspect of the cycle. Additionally, at least the heat is being added at the correct phase of the cycle. However, the low temperature constant pressure process is not part of the Carnot Cycle and will therefore detract from the efficiency. The efficiency of the Brayton Cycle is given by:
  η  =            1      -                        T          1                          T          2                      =          1      -              1                  r                      γ            -            1                              Note that this is identical to the theoretical efficiency of the Otto Cycle. This supports the previous statement that claimed there should be an improvement from the high temperature and pressure constant pressure phase (“2”-“5” in FIGS. 7a and 7b) because it adds heat at the right time. But there will be a degradation in efficiency from the low pressure & temperature constant pressure phase (“6”-“1” in FIGS. 7a and 7b). The Humphrey Cycle is also shown in FIGS. 6a and 6b for comparison. It suffers the same ills (as far as efficiency is concerned) as the Otto Cycle from point “2” to point “3”, and the same problem as the Brayton Cycle from point “4” to point “1”. Its efficiency is given by:
  η  =      1    -          γ      ⁢                        T          1                          T          2                    ⁢                                                  (                                                T                  3                                                  T                  2                                            )                                      1              /              γ                                -          1                                                    T              3                                      T              2                                -          1                    This is a more complex expression than the others so far, but at its core the T1/T2 factor tells us its comparable to the Otto cycle. Additionally, the structure of the other terms have a form that is complementary to the Diesel efficiency equation with appropriate conversion of the temperatures to compression ratio. This is due to the symmetry of the P-V plot's constant pressure phase “4”-“1” path bearing a complementary relation to the constant pressure path in the Diesel Cycle. Where the Humphrey Cycle may pick up some advantage is from realistic instantiation, where T3 can be made quite high. This reduces the magnitude of the subtracted term, thereby yielding a higher efficiency value. But unless T3 is high, it is not much more efficient than the other cycles, and still much less efficient than a Carnot Cycle.New Emerging Higher Efficiency Engines
The prior sections focused on the most common and least efficient engines. This section presents a very short discussion on two other emerging thermal engine cycles with higher potential efficiency: the Stirling Cycle and the Ericsson Cycle engines.
The Internet is rich with information on the Stirling engine which will not be repeated here. Suffice it to say that the Stirling engine is an external combustion closed cycle engine which in fact does a better job of emulating a Carnot Cycle (at least by comparison to the prior engines discussed so far). The Ericsson engine by contrast is a bit less well known. It also uses external combustion but with an open cycle that otherwise bears several similarities to the Stirling engine both in design and in efficiency. There have been some new designs in recent years that increase its potential on par with Stirling engines.
Our key reason for mentioning the Stirling and Ericsson cycle engines is that they both have a particularly interesting attribute in common with the Carnot cycle: they both have the same theoretical efficiency as the Cartnot Cycle! The key difference is that their temperature-entropy plots (T-S) are parallelograms, whereas the Carnot Cycle is a rectangle. For the Stirling Cycle the Parallelogram of the T-S plot slants to the right (toward higher entropy change) and for the Erickson it slants towards the left (toward lower entropy change). But for the same Tc and Th, the area under both the rectangle T-S plot of the Carnot Cyle or parallelogram T-S plots of the Stirling and Erickson Cycles is the same, and therefore so too are their efficiencies.
So if the Stirling and Ericsson cycles have the same theoretical efficiency as the Carnot cycle, why not just use them? Indeed, with the recent rise in fuel costs several efforts are underway to do just that. But there are implementation issues with both the Stirling and Ericsson engines. Both are external combustion engines. This is often considered a key advantage in a globally warming world, since it is usually presumed that external combustion will produce less pollution than internal combustion. But there are still challenges with obtaining a truly efficient external burner and regenerative heat exchangers. And if the burners/exchangers are not efficient enough (currently the case) then maximum efficiency cannot be realized. Additionally, less efficient burners/exchangers can also present pollution problems, although this is considered less challenging than with internal combustion
Perhaps most important though is that external combustion imposes limits on cold start availability and load following. These two engines need to “warm up” before they can supply power. The startup time might not be all that much of an imposition with additional engineering, but in an impatient world, every second counts off points against the design. The load following limitation is perhaps the more stressing problem because it limits the applications these engines can be applied to. For example, activating an electric space heater places a dramatic load change on a 1.5 kW generator, which is easy for a gasoline or Diesel engine to follow, but very challenging for a Stirling or Ericsson engine to follow.
Finally, a closer examination of these cycles reveals that they both tend to “clip the corners” of the ideal theoretical cycle diagram (as do many engines). This is paramount to deviating from the theoretically optimum thermal cycles in a manner not unlike the way the Otto and Diesel cycles deviate from the Carnot cycle. The result is further reduction in efficiency from that which would otherwise be expected.
Summary and Assessment of Common Conventional Thermal Engines
The sections above have given P-V and T-S plots for the more common thermal cycles. These are the main cycles that companies spend millions of dollars on each year trying to improve the efficiency of. With the exception of the Stirling and Ericsson cycles, all these cycles bear more resemblance to each other than they do to the Carnot Cycle which they should attempt to emulate: sometimes these cycles even share the exact same efficiency equation, none of which is the Carnot Cycle's efficiency equation.
The reasons that these engines deviate from a true Carnot are both historical and pragmatic. Yet, after over 100 years of thermal engine development few of these cycles bear anything but a passing resemblance to the Carnot Cycle that they must follow for optimum efficiency. None of them does a good job emulating the Carnot Cycle. In some cases heat is not even added or removed during the correct phase of the cycle. In other cases the cycles deviate significantly from a Carnot Cycle. In all cases none of these cycles contain the correct isothermal and adiabatic processes needed during the compression and expansion strokes of a true Carnot Cycle.
The Stirling and Ericsson cycles have the same theoretical efficiency as the Carnot cycle, but they suffer from cold start and load following problems due to the latency of their external combustion heat source. Furthermore, both the external combustor and the details of the cycle implementation limit them from achieving their true theoretical efficiency.
The conclusion from these observations is that we should not be at all surprised that most thermal engines today have less than optimum thermal efficiency. There are many factors (mechanical friction, fuel combustion, fluid drag, etc.) that can degrade efficiency. But if one starts with a theoretically lower than optimum efficiency design, there can be no hope of making significant improvements in efficiency afterwards. We need a new fresh approach to deriving high efficiency from thermal engines, and Carnot has already told us what it needs to be: a Carnot Cycle.